Polyatomic Molecule Vibrations and Fourier Series – Rankers Physics

Equation of SHM: Practice Problem & Solution

Assertion (A): General vibrations of a polyatomic molecule about its equilibrium position is periodic but not SHM. Reason (R): A periodic motion can always be expressed as a sum of infinite number of harmonic motion with appropriated amplitude.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. Complex vibrations of polyatomic molecules are periodic but generally not simple harmonic motion (SHM). Reason (R) is true. This is the principle of Fourier analysis, stating that any periodic motion can be decomposed into a sum of simple harmonic components. Reason (R) correctly explains why complex periodic motions (like polyatomic vibrations) are not SHM but can still be described as periodic.

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1. For the damped oscillator, if time taken for its amplitude of vibrations to drop to half of its initial value is \(T\) then time taken for amplitude to drop to one eighth amplitude is
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